Chapter 4, Problem 146CR

To determine

To Find : The equation modelling the motion of the bobber.

Answer to Problem 146CR

The equation modelling the motion of the bobber is, $y=3.5\cos (\Pi t)$

Explanation of Solution

Given information : The fishing bobber is oscillating in a simple harmonic motion. The total distance travelled by the bobber vertically is 7 inches from the high point to low point.And the high point corresponds to time, t = 0.

As the high point of the bobber corresponds to time t = 0, the function representing the distance travelled by buoy will be a cosine function.

That is,

  $y=A\cos (\omega t)$ .......(1)

Where, A represents the amplitude, $\omega$ represents the angular velocity of the bobber and T is the time period and t is the time.

Since amplitude A of a simple harmonic motion represents the vertical displacement towards both the sides. Therefore the vertical distance from high to low point covers twice the amplitude.

Therefore, A = 3.5 inches.

As time period T = 2 sec, the angular velocity is,

  $\omega =\frac{2\Pi }{T}=\frac{2\Pi }{2}=\Pi$ .

By substituting $\omega$ and A in equation number (1), implies,

  $y=3.5\cos (\Pi t)$ .

Thus,

The equation representing the distance travelled by the bobber is,

  $y=3.5\cos (\Pi t)$